"Non-Euclidean Geometry is a history of the alternate geometries
that have emerged since the rejection of Euclid s parallel
postulate. Italian mathematician ROBERTO BONOLA (1874 1911) begins
by surveying efforts by Greek, Arab, and Renaissance mathematicians
to close the gap in Euclid s axiom. Then, starting with the 17th
century, as mathematicians began to question whether it was
actually possible to prove Euclid s postulate, he examines
non-Euclidean predecessors Saccheri, Lambert, Legendre, W. Bolyai,
Wachter, and Thibaut, and non-Euclidean founders Gauss, Schweikart,
Taurinus, Lobachevski, and J. Bolyai. He concludes with a look at
later developments in non-Euclidean geometry. Including five
appendices and an index of authors, Bonola s Non-Euclidean Geometry
is a useful reference guide for students of mathematical history."
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